Sodium ion hybrid supercapacitor temperature real-time prediction method

Abstract

The invention belongs to the technical field of sodion hybrid supercapacitor temperature detection, and particularly relates to a sodion hybrid supercapacitor temperature real-time prediction method. According to the method, a two-stage Gaussian process fusion framework for physically guiding machine learning is constructed; a first-stage Gaussian process model establishes a quantitative mapping relation between capacitor operation parameters and capacitor heating power through physical constraints; the second-stage dynamic Gaussian process model is combined with the capacitor heating power to accurately predict temperature evolution in real time; according to the method, through an intermediate variable embedding strategy guided by a physical mechanism, the limitation of a traditional data-driven model is broken through, and under the condition that the sample size is reduced by 40%, the prediction precision of 0.985 or above is still kept; only three basic parameters of current, voltage and environment temperature need to be monitored, and the sensor deployment complexity is reduced; the method can be applied to a heat management system of an electric automobile capacitor bank and a novel energy storage system, and provides technical support for design of the energy storage system.

Description

Technical Field

[0001] The present invention belongs to the technical field of temperature detection of sodium-ion hybrid supercapacitors, and particularly relates to a method for real-time prediction of the temperature of sodium-ion hybrid supercapacitors. Specifically, aiming at the thermal behavior prediction requirements of sodium-ion hybrid supercapacitors under unsteady charge and discharge conditions, a real-time prediction framework of the temperature field with physical interpretability is constructed by combining multi-physics field coupling modeling and dynamic Gaussian process regression technology, which is applicable to the optimal design of thermal management systems in scenarios such as electric vehicle capacitor banks and grid-level energy storage systems. Background Art

[0002] As a new generation of electrochemical energy storage devices, sodium-ion hybrid supercapacitors have the dual characteristics of electrochemical batteries and supercapacitors. With their high power density, wide temperature range characteristics and resource sustainability advantages, they show important application values in transient high-power scenarios such as rail transit energy recovery and power grid frequency modulation. However, its thermal safety issue is still an outstanding bottleneck restricting large-scale applications: during frequent charge and discharge processes, the non-linear superposition of electrode polarization heat and ohmic heat will cause the local temperature to rise sharply (exceeding 80 °C), triggering chain reactions such as electrolyte decomposition and interface SEI film rupture, and in severe cases, it can cause permanent damage to the device.

[0003] Currently, the temperature monitoring technology for sodium-ion hybrid supercapacitors mainly faces three major challenges: (1) Inaccurate prediction model: Traditional data-driven methods rely on a large amount of historical data for training. However, under unsteady conditions such as emergency braking of vehicles, due to the current mutation rate exceeding 10³ A / s, the prediction lag exceeds 5 seconds, which cannot meet the real-time warning requirements; (2) High sensing cost: Existing solutions require the deployment of 8 types of detection devices such as internal temperature sensors and strain gauges, increasing the module cost by more than 40%; (3) Insufficient mechanism integration: Although pure physical models can describe the heat conduction path, their solution requires iterative calculation of more than 3000 grid nodes, resulting in a single prediction time exceeding 15 minutes, making it difficult to integrate into an embedded BMS system.

[0004] Especially in the grid-level energy storage scenario, when facing random charge and discharge shocks caused by renewable energy fluctuations, existing temperature prediction methods generally have a steady-state error of more than ±4 °C, while the safe temperature rise threshold of sodium-ion devices is only ±1.5 °C. Therefore, there is an urgent need to develop a temperature real-time prediction method with both physical mechanism interpretability and machine learning adaptability to break through the thermal management technology bottleneck under complex conditions. Summary of the Invention

[0005] The purpose of the present invention is to overcome the deficiencies in the prior art and provide a method for real-time prediction of the temperature of sodium-ion hybrid supercapacitors.

[0006] To achieve the object of the present invention, the present invention is implemented by the following technical solutions.

[0007] A real-time temperature prediction method for a sodium-ion hybrid supercapacitor, comprising the following steps: S1. Based on a real capacitor bank and its thermal management system, a multi-physics field coupling finite element model is established, and the relationships among the capacitor operating parameters, the heating power, and the temperature during the capacitor operation are quantitatively simulated through finite element simulation; wherein: the operating parameters include current, voltage, and ambient temperature; S2. Collect and summarize the results of the operating parameters, the heating power, and the temperature varying with time during the capacitor operation quantitatively simulated by the finite element simulation to form a training data set (A, B, C), wherein: A is the input parameter, B is the key intermediate variable, and C is the output parameter; S3. Select the (A, B) part in the training data set (A, B, C) as the training data, with the input parameter A as the input , and the key intermediate variable B as the output , and a quantitative mapping relationship between the input parameter A and the key intermediate variable B is established by training a first-level Gaussian process surrogate model; wherein: the expression of the first-level Gaussian process surrogate model is: , In the formula, μ is the mean value; is a Gaussian random process function with a mean of zero and a variance of σ 2 , and its covariance matrix is: , In the formula, R( x i , x j ) is the correlation matrix of the input parameters x i and x j , wherein: a p and b p are model coefficients, and k is the number of input parameters x; S4. Using the training data set (A, B, C) as the training data, with the data set matrix [A, B] formed by adding the input parameter A and the key intermediate variable B as the input , and the output parameter C as the output , and a quantitative mapping relationship among the input parameter A, the key intermediate variable B, and the output parameter C is established by training a second-level Gaussian process surrogate model; wherein: the expression of the second-level Gaussian process surrogate model is: , In the formula, μ 2 is the mean value, is a Gaussian random process function with a mean of zero and a variance of σ 2 ; S5. Use the trained first-level Gaussian process surrogate model and the second-level Gaussian process surrogate model to predict the output value Y(x') of any new input point x', and it follows a normal distribution of the mean and covariance normal distribution variables ; where: The mean is: , where r is the correlation vector between x' and x, represents the correlation matrix, and N is an n×1 unit vector; The covariance normal distribution variable has the following expression: .

[0008] As a preferred embodiment of the present invention, the control equations of the multi-physical field coupling finite element model include: , , , , , , , where c is the sodium ion concentration, D is the sodium ion conductivity, J is the sodium ion conduction flux, I n is the electrochemical reaction current density, F is the Faraday constant, I 0 is the exchange current density, α a and α c are the charge exchange coefficients of the oxidation and reduction reactions respectively, η p is the overpotential, R and T are the ideal gas constant and the temperature respectively, Q tot is the capacitive heat generation power, Q r andQ ohm They are capacitive reaction heat and Joule heat respectively, I l and I s They are the current densities of the electrolyte and the electrode respectively, Φ l and Φ s They are the electric potentials of the electrolyte and the electrode respectively, ρ, C p 、k are the density, specific heat capacity and thermal conductivity of the material.

[0009] As a preferred solution of the present invention, the multi-physical field coupling finite element model includes: an electrochemical field finite element model for simulating the electrochemical reactions, electron transfer and heat generation processes occurring during the charging and discharging of the capacitor bank, and a solid heat transfer field finite element model for calculating the temperature changes of the capacitor bank and the cooling system.

[0010] As a preferred solution of the present invention, the heat generation process includes Joule heat and polarization heat.

[0011] As a preferred solution of the present invention, the input parameters are the real-time operating parameters of the capacitor, namely the real-time current of the capacitor, the real-time voltage of the capacitor and the real-time ambient temperature of the capacitor; the key intermediate variable is the heat generation power of the capacitor; the output parameter is the real-time temperature of the capacitor.

[0012] As a preferred solution of the present invention, it further includes a method for improving the fidelity of the first-level Gaussian process surrogate model and the second-level Gaussian process surrogate model : An adaptive sampling method is adopted to extract the data point x' with the maximum prediction uncertainty in the input parameter space, and substitute it into the multi-physical field finite element model in step S1 to obtain its corresponding data point (A', B', C), and update the training data set, and iterate on the first-level Gaussian process surrogate model and the second-level Gaussian process surrogate model and the second-level Gaussian process surrogate model for iteration.

[0013] As a preferred solution of the present invention, the specific method for improving the fidelity of the first-level Gaussian process surrogate model and the second-level Gaussian process surrogate model includes the following steps: S61. In the input parameter space, select N (N is a natural number) key sample points x* with the maximum covariance , and substitute them into the multi-physical field coupling finite element model in step S1 to obtain their corresponding data points Y*; S62. Supplement (x*, Y*) to the training dataset (X, Y), and repeat steps S3 to S4 to iteratively update the first-level Gaussian process surrogate model and the second-level ; S63. Repeat steps S61 and S62 until the relative error of the key sample point x* is less than 0.01, that is, it is determined that the first-level Gaussian process model and the second-level Gaussian process surrogate model have high fidelity.

[0014] As a preferred solution of the present invention, key sample points are selected in the mutation region where the current gradient dI / dt > 100 A / s.

[0015] As a preferred solution of the present invention, the specific implementation process of step S5 includes the following steps: S91. Take the capacitance operating parameters (I, V, T) as the input parameter A, and the capacitance heating power Q as the key intermediate variable B. Substitute A into the first-level Gaussian process surrogate model to obtain B, that is, the predicted result Q of the capacitance heating power pred ; S92. Take the capacitance operating parameters (I, V, T) as the input parameter A, the predicted result Q of the first-level Gaussian process surrogate model pred as the key intermediate variable B, and the capacitance temperature T as the output parameter C. Substitute [A, B] into the second-level Gaussian process surrogate model to obtain the output parameter C, that is, the real-time capacitance temperature under non-steady-state charge and discharge conditions.

[0016] Beneficial effects: Through the intermediate variable embedding strategy guided by physical mechanisms, the present invention breaks through the "black box" limitation of traditional data-driven models and still maintains a prediction accuracy of more than 0.985 when the sample size is reduced by 40%; the present invention establishes a prediction paradigm for non-steady-state conditions and supports the temperature field reconstruction of large-fluctuation charge and discharge scenarios; the present invention only needs to monitor three basic parameters of current, voltage, and ambient temperature, significantly reducing the complexity of sensor deployment; the present invention can be applied to the thermal management system optimization of electric vehicle capacitor banks and new energy storage systems, providing key technical support for the design of high-safety energy storage systems. Description of the Drawings

[0017] Figure 1 is the flowchart of the method described in the present invention; Figure 2 is the schematic diagram of the dynamic operating conditions of the capacitor module described in the present invention; Figure 3The real-time temperature change trend graph of the battery cell predicted by the method of the present invention. Detailed implementation manners

[0018] The present invention will be further described in conjunction with the embodiments and the accompanying drawings.

[0019] As Embodiment 1 of the present invention, the real-time prediction of the temperature of the sodium-ion hybrid supercapacitor during the emergency braking of an electric vehicle.

[0020] For the sodium-ion hybrid supercapacitor bank (including 10 single capacitors and equipped with a liquid-cooled thermal management system) of an electric vehicle under the emergency braking condition, it is necessary to predict the temperature change caused by large-current discharge (energy recovery) in real time to avoid safety risks caused by local overheating.

[0021] 1. Emergency braking condition parameters Current gradient: dI / dt = -200 A / s; Input parameter range: Real-time current (I): -200 A; Real-time voltage (U): 2.8 V; Ambient temperature (T1): 25 °C 2. Construction of the multi-physics coupling finite element model: (1). Model composition: Electrochemical field finite element model: Simulate the electrochemical reaction (sodium ion insertion / extraction, electron transfer) and polarization heat generation during emergency braking. The control equations include: Sodium ion concentration diffusion equation: , Electrochemical reaction current density: , Solid heat transfer field finite element model: Calculate the heat exchange between the capacitor bank and the coolant. Control equation: , where: total heat generation power .

[0022] . Input and output definitions: Input parameter A: (I, U, T1) = (-200 A, 2.8 V, 25 °C); Key intermediate variable B: Heat generation power Q, including the surge of Joule heat caused by high-frequency pulsed current during braking; Output parameter C: Real-time temperature T of the battery cell; 3. Generation of the training data set (1). Data collection Simulation conditions: Simulate the emergency braking process in COMSOL for a duration of 10 s with a time interval of 1 s to generate 200 groups of emergency braking data, including: Current I: Drops suddenly from 0 A to -200 A; Voltage U: Drops rapidly from 3.5 V to 2.8 V; Heating power Q: Obtained through finite element calculation, including 70% of Joule heat and 30% of polarization heat; Dataset format: Training dataset = , including 200 sets of emergency braking data + 1800 sets of other working condition data.

[0023] 4. Training of the two-stage Gaussian process model (1) Training of the first-stage Gaussian process surrogate model: Model structure: Adopts a squared exponential kernel function, covariance matrix: , where k = 3, corresponding to the three input parameters I, U, and T1.

[0024] (2) Training process: Input: (I, U, T1) under emergency braking conditions; Output: Measured heating power Q Optimization goal: Minimize the root mean square error RMSE ≤ 2 W, and adjust the hyperparameters through maximum likelihood estimation .

[0025] (3) Training of the second-stage Gaussian process surrogate model: Model structure: The input dimension is expanded to 4D (I, U, T1, Q), and the kernel function is the same as that of the first stage.

[0026] (4) Training process: Input: (I, U, T1, Q) during emergency braking; Output: Measured cell temperature T; Optimization goal: Minimize the temperature prediction error, and the RMSE of the validation set ≤ 0.5 °C.

[0027] 5. Temperature real-time prediction process: Step 1: Prediction of heating power: Input: Real-time parameters of emergency braking A' = (-200 A, 2.8 V, 25 °C) Calculation: Output the predicted heating power through the first-stage Gaussian process surrogate model G GP-1 (x) , which includes the power peak at the moment of braking.

[0028] Step 2: Real-time temperature prediction: Input: Concatenated data

[0029] Calculation: Through the second-stage Gaussian process surrogate model GGP-2 (x) Output real-time temperature , with a prediction lag time < 1 s, meeting the real-time warning requirement.

[0030] 6. Model fidelity optimization: Selection of key sample points: Region: The emergency braking mutation region with a current gradient dI / dt > 100 A / s, such as within 0 - 2 s after the start of braking.

[0031] Method: Calculate the covariance value of the prediction uncertainty e(x') for each point in this region, and select the first 5 points with the largest uncertainty as x*.

[0032] Iterative optimization process: Data supplementation: Substitute x* into the finite element model to obtain real data (A*, B*, C*), such as comparing the measured temperature of 29.0 °C at the braking peak point with the predicted value of 28.5 °C.

[0033] Model update: Add the new data to the training set, and repeat steps S3 - S4 until the relative error of the key sample points , and it converges after about 3 iterations.

[0034] 7. Implementation effect verification: Sensor deployment: Only 3 types of sensors are required: current sensor (measurement range ±200 A), voltage sensor (2.8 V - 3.5 V), ambient temperature sensor (-20 °C - 60 °C), reducing 5 types of sensors compared to the traditional scheme and reducing the cost by 40%.

[0035] Prediction performance: Steady-state error: ±1.0 °C, superior to ±4 °C of the traditional method.

[0036] Non-steady-state response: The temperature prediction lag during emergency braking < 1 s, accurately capturing the temperature peak within 3 s after the start of braking. The measured peak is 29.2 °C, the predicted value is 29.0 °C, and the error is 0.68%.

[0037] Under small-sample working conditions such as emergency braking (with a 40% reduction in the sample size), the prediction accuracy R 2 > 0.985, breaking through the dependence of the pure data-driven model on historical data.

[0038] During emergency braking, the input parameters (I = -200 A, U = 2.8 V, T1 = 25 °C) are output as Q = 150 W by the first-level Gaussian process surrogate model, and then the input parameters (I = -200 A, U = 2.8 V, T1 = 25 °C, Q = 150 W) are output as the real-time temperature T = 28.5 °C by the second-level Gaussian process surrogate model, as Figure 1 shown.

[0039] During the emergency braking phase, the current suddenly drops below -200 A, and the voltage quickly drops to 2.8 V, corresponding to the boundary conditions of the model input, such as Figure 2 shown.

[0040] Within 0 - 5 s after braking starts, the model-predicted temperature is highly consistent with the measured temperature, verifying the effectiveness of the adaptive sampling strategy under mutation conditions, such as Figure 3 shown.

[0041] As Example 2 of the present invention, real-time temperature prediction of a sodium-ion hybrid supercapacitor during constant current charge and discharge.

[0042] For a sodium-ion hybrid supercapacitor bank (including 10 single capacitors equipped with a liquid-cooled thermal management system) in an electric vehicle under constant current charge and discharge conditions, it is necessary to predict the temperature evolution process under a constant current in real time to avoid the risk of temperature exceeding the limit due to continuous heating.

[0043] 1. Operating parameters Constant current charging: current I = 100 A (charging state), duration: 300 s; Constant current discharging: current I = -100 A (discharging state), duration: 300 s; Input parameter range: Real-time voltage U: 2.8 V → 3.5 V during the charging stage, 3.5 V → 2.8 V during the discharging stage; Ambient temperature T1 = 25 °C, normal temperature condition; Current gradient: dI / dt = 0 A / s, constant current, no mutation; 2. Construction of a multi-physics coupling finite element model Model composition Electrochemical field finite element model: Simulate the sodium ion insertion / extraction, electron transfer, and polarization heat generation during constant current charge and discharge. The governing equations include: Sodium ion concentration diffusion equation: , Electrochemical reaction current density: , during constant current charge and discharge, the overpotential varies linearly with the voltage; Solid heat transfer field finite element model: Calculate the steady-state heat exchange between the capacitor bank and the coolant. Governing equation: , where: total heat generation power ; where: Joule heat Q ohm is proportional to the square of the current, and polarization heat Q r is related to the electrochemical reaction rate.

[0044] Input / output definition: Input parameter A: (I, U, T1) = (100 A / -100 A, U, 25 °C); Key intermediate variable B: Heating power Q, mainly Joule heat in the constant current scenario, accounting for about 80%; Output parameter C: Real-time temperature T of the battery cell; 3. Training dataset generation: Data collection Simulation conditions: Simulate the constant current charging (100 A) and discharging (-100 A) processes in COMSOL with a time interval of 1 s, generating a total of 1000 groups of data (500 groups for charging + 500 groups for discharging).

[0045] Data included: Current I: Fixed at 100 A or -100 A; Voltage U: Rises from 2.8 V to 3.5 V during charging and drops from 3.5 V to 2.8 V during discharging; Heating power Q: Obtained through finite element calculation, Q ≈ 80 W during charging and Q ≈ 75 W during discharging, with slight differences due to polarization effects; Dataset format: Training dataset = , including 1000 groups of constant current data + 1000 groups of data under other working conditions.

[0046] Training of the two-stage Gaussian process model Training of the first-stage Gaussian process surrogate model Model structure: Using the squared exponential kernel function, covariance matrix: , where k = 3, corresponding to the three input parameters I, U, and T1.

[0047] Training process: Input: (I, U, T1) under the constant current condition; Output: Measured heating power Q Optimization objective: Minimize the root mean square error RMSE ≤ 1.5 W, and adjust the hyperparameters through maximum likelihood estimation .

[0048] Training of the second-stage Gaussian process surrogate model Model structure: The input dimension is expanded to 4D (I, U, T1, Q), and the kernel function is the same as that of the first stage.

[0049] Training process: Input: (I, U, T1, Q) during constant current; Output: Measured temperature T of the battery cell; Optimization objective: Minimize the temperature prediction error, with the RMSE of the validation set ≤ 0.3°C, the temperature change being gentle under the constant current scenario, and higher accuracy.

[0050] 5. Real-time prediction process: Step 1: Prediction of heating power: Input: Real-time parameters of constant current charge and discharge A'=(100A / -100A, U', 25°C) Calculation: Output the predicted heating power Q through the first-level Gaussian process surrogate model G GP-1 (x) pred .

[0051] Charging scenario: Q pred = 80.5W, with the error from the simulation value ≤ 1%; Discharging scenario: Q pred = 76.2W, with the error from the simulation value ≤ 1.6%; Step 2: Real-time temperature prediction: Input: Concatenated data x' = [A', Q pred = (I', U', 25°C, Q pred ); Calculation: Output the real-time temperature T through the second-level Gaussian process surrogate model G GP-2 (x) pred .

[0052] Charging stage: Initial temperature 25°C, predicted temperature 32.5°C after 300s, measured 32.8°C, error 0.9%; Discharging stage: Initial temperature 32.5°C, predicted temperature 27.0°C after 300s, measured 26.8°C, error 0.7%; 6. Optimization of model fidelity Selection of key sample points Region: Under the constant current condition, the current gradient dI / dt = 0A / s, but sample points need to be selected when the voltage is close to the cut-off value, such as when charging to 3.5V and discharging to 2.8V, because the polarization effect is significant and the temperature change rate is high at this time.

[0053] Method: Calculate the prediction uncertainty e(x') of the voltage boundary point, and select the first 3 points with the largest uncertainty as x*.

[0054] Iterative optimization process Data supplementation: Substitute x* into the finite element model to obtain real data, such as the measured temperature of 33.0°C and the predicted value of 32.5°C at the end of charging.

[0055] Model update: Add the new data to the training set, and repeat steps S3 - S4 until the relative error of the key sample points < 0.01, usually 1 - 2 iterations are required for convergence.

[0056] 7. Implementation effect verification: Sensor deployment: Only three types of sensors are required: current sensors (±200A), voltage sensors (2.8V - 3.5V), and ambient temperature sensors (-20°C - 60°C), reducing five types of sensors compared to the traditional solution and lowering the cost by 40% compared to the traditional solution.

[0057] Prediction performance: Steady-state error: ±0.5°C. In the constant current scenario, the temperature changes smoothly, and the error is significantly lower than that in the non-steady-state working conditions.

[0058] Response time: The prediction lag time < 0.5s. In the constant current working condition, there is no sudden change in current, and the calculation efficiency is higher.

[0059] Accuracy verification: In the temperature curve, the coincidence degree between the model prediction curve and the measured temperature reaches 99% in the constant current charging stage and 98.5% in the discharging stage, as shown in Figure 3 shown.

[0060] Utilize the physical laws under the constant current condition, such as Joule heat Q ∝ I 2 Constrain the first-level model to reduce the dependence on a large amount of data. When the proportion of constant current data is only 50%, the R 2 > 0.99 prediction accuracy is still maintained.

[0061] During constant current charge and discharge, input parameters: such as (I = 100A, U = 3.0V, T1 = 25°C) are output as Q = 80W by the first-level Gaussian process surrogate model, and then input (I = 100A, U = 3.0V, T1 = 25°C, Q = 80W) to output the real-time temperature T = 28.5°C by the second-level Gaussian process surrogate model, as shown in Figure 1 shown.

[0062] During the constant current stage, the current remains at 100A / -100A, and the voltage changes linearly, corresponding to the stable working condition of the model input.

[0063] During constant current charging, the temperature rises uniformly, and during discharging, it drops uniformly. The model prediction curve and the measured curve almost coincide, verifying the high-precision prediction ability under steady-state working conditions.

[0064] Through the above embodiments, based on the dual-level Gaussian process fusion framework and physical mechanism constraints, high-precision real-time prediction of the temperature of sodium-ion hybrid supercapacitors during constant current charge and discharge is achieved, providing a reliable engineering solution for the thermal management of energy storage systems.

[0065] The preferred embodiments of the embodiments of the present application have been described above with reference to the accompanying drawings, which do not limit the scope of the rights of the embodiments of the present application. Any modifications, equivalent substitutions, and improvements made by those skilled in the art without departing from the scope and essence of the embodiments of the present application shall fall within the scope of the rights of the embodiments of the present application.

Claims

1. A method for real-time prediction of temperature of a sodium ion hybrid supercapacitor, characterized in that: The following steps are involved: S1. According to the real capacitor group and its thermal management system, a multi-physics field coupling finite element model is established, and the relationship between the operating parameters, heating power and temperature during the operation of the capacitor is simulated by finite element simulation; wherein: the operating parameters include current Ι, voltage V and ambient temperature ℃; S2. By collecting and summarizing the results of the operation parameters, heating power and temperature changes over time during the simulation process, a training data set (A, B, C) is formed, where A is the input parameter, B is the key intermediate variable, and C is the output parameter; S3, select the (A, B) part of the training data set (A, B, C) as the training data, with A as the input , B is the output , train the first-level Gaussian process proxy model to establish a quantitative mapping relationship between A and B; where: the first-level Gaussian process proxy model is: ， Where μ is the average value; is zero and has a variance of σ 2 The Gaussian random process function has a covariance matrix of: ， In the formula, R( x i , x j ) is the input parameter x i and x j The correlation matrix of p and b p are the model coefficients, k is the number of input parameters x; S4. Take the training data set (A, B, C) as the training data, and add A and B to form the data set matrix [A, B] as the input , C is the output , train the second-level Gaussian process proxy model to establish a quantitative mapping relationship between A, B and C; where: the second-level Gaussian process proxy model is: ， Where μ2 is the average value, is zero and has a variance of σ 2 Gaussian random process function; S5. Use the trained first-level Gaussian process proxy model and the second-level Gaussian process surrogate model Predict the output value Y(x') of any new input point x' and obey the average value and covariance of normally distributed variables ;in: average value for: ， Where r is the correlation vector between x' and x, represents the correlation matrix, N is an n×1 unit vector; Covariance Normally Distributed Variables for: 。 2. The method for real-time temperature prediction of a sodium ion hybrid supercapacitor according to claim 1, characterized in that: The control equations of the multi-physics field coupled finite element model include: ， ， ， ， ， ， ， In the formula, c is the sodium ion concentration, D is the sodium ion conductivity, J is the sodium ion conduction flux, I n is the electrochemical reaction current density, F is Faraday's constant, I 0 is the exchange current density, α a and α c are the charge exchange coefficients for oxidation and reduction reactions, respectively, η p is the overpotential, R and T are the ideal gas constant and temperature, Q tot is the heat generation power of the capacitor, Q r and Q ohm are the capacitive reaction heat and the Joule heat, I l and I s are the current densities of the electrolyte and the electrode, respectively, Φ l and Φ s are the potentials of the electrolyte and the electrode, respectively, ρ、C p 、k are the density, specific heat capacity and thermal conductivity of the material.

3. A method for real-time prediction of temperature of a sodium ion hybrid supercapacitor according to claim 2, characterized in that: The multi-physics field coupled finite element model includes: an electrochemical field finite element model for simulating electrochemical reactions, electron transfer and heat generation processes occurring during the charging and discharging process of the capacitor group, and a solid heat transfer field finite element model for calculating the temperature changes of the capacitor group and the cooling system.

4. A method for real-time prediction of temperature of a sodium ion hybrid supercapacitor according to claim 3, characterized in that: The heat generation process includes Joule heat and polarization heat.

5. The method for real-time temperature prediction of a sodium ion hybrid supercapacitor according to claim 1, characterized in that: The input parameters are the real-time operating parameters of the capacitor, namely, the real-time current of the capacitor, the real-time voltage of the capacitor and the real-time ambient temperature of the capacitor; the key intermediate variable is the heating power of the capacitor; and the output parameter is the real-time temperature of the capacitor.

6. The method for real-time temperature prediction of a sodium ion hybrid supercapacitor according to claim 1, characterized in that: It also includes improving the first-level Gaussian process surrogate model and the second-level Gaussian process surrogate model Fidelity method: Adaptive sampling method is used to extract the input parameter space with the largest prediction uncertainty The data point x' is taken and brought into the multi-physics finite element model in step S1 to obtain its corresponding data point (A', B', C), and the training data set is updated to perform the first-level Gaussian process proxy model and the second-level Gaussian process surrogate model Iterate.

7. A method for real-time prediction of temperature of a sodium ion hybrid supercapacitor according to claim 6, characterized in that: The first-level Gaussian process agent model is improved and the second-level Gaussian process surrogate model The specific method of fidelity includes the following steps: S61. In the input parameter space, select the one with the largest covariance N (N is a natural number) key sample points x* are obtained, and are brought into the multi-physics field coupling finite element model in step S1 to obtain the corresponding data points Y*; S62, add (x*, Y*) to the training data set (X, Y), and repeat steps S3 to S4 to train the first-level Gaussian process proxy model and second level Perform iterative updates; S63, repeat steps S61 and S62 until the relative error of the key sample point x* is less than 0.01, that is, the first-level Gaussian process model is identified. and the second-level Gaussian process surrogate model With high fidelity.

8. A method for real-time prediction of temperature of a sodium ion hybrid supercapacitor according to claim 6, characterized in that: Select key sample points in the mutation area of ​​current gradient dI / dt>100 A / s.

9. The method for real-time prediction of temperature of a sodium ion hybrid supercapacitor according to claim 1, characterized in that: The specific implementation process of step S5 includes the following steps: S91. Take the capacitor operating parameters (I, V, T) as input parameter A and the capacitor heating power Q as the key intermediate variable B, and substitute A into the first-level Gaussian process proxy model. , to obtain B, which is the predicted result of the capacitor heating power Q pred ; S92, taking the capacitor operating parameters (I, V, T) as input parameters A, the first-level Gaussian process proxy model The prediction result Q pred As the intermediate variable B, the capacitance temperature T as the output parameter C, [A, B] is substituted into the second-level Gaussian process agent model To obtain the output parameter C, that is, the real-time temperature of the capacitor under non-steady-state charging and discharging conditions.

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